Perceptron Playground

Visualize how perceptrons learn linear decision boundaries

Click: add class 0 (white) • Shift+Click: add class 1 (black)

Parameters

Learning Rate: 0.10

w₁ = 0.500

w₂ = -0.300

b = 0.100

Controls

Statistics

Epoch	0
Accuracy	0.0%
Points	0

Theory

The perceptron finds a linear decision boundary w₁x + w₂y + b = 0 that separates two classes.

For each misclassified point, weights are updated: w ← w + α·y·x, where α is the learning rate and y is the true label.

The algorithm converges if data is linearly separable. For non-separable data, it oscillates.

Key Concepts

Linear Separability: Data that can be separated by a straight line (hyperplane).
Decision Boundary: The line w₁x + w₂y + b = 0 that divides the two classes.
Learning Rate α: Controls step size during weight updates. Too high causes oscillation.
Convergence: Guaranteed for linearly separable data within finite iterations.

Experiments

1. Linear data: Create two clearly separated clusters. The perceptron should find a boundary quickly.
2. XOR pattern: Place points at corners: (−1,−1), (1,1) as one class and (−1,1), (1,−1) as another. Observe non-convergence.
3. Margin effects: Create data with different margins. Wider margins lead to more stable boundaries.
4. Learning rates: Compare α=0.01 vs α=1.0. High rates may overshoot optimal weights.

Historical Context

Frank Rosenblatt introduced the perceptron in 1957 at Cornell Aeronautical Laboratory. Initially hyped as a breakthrough toward artificial intelligence, it faced criticism after Minsky and Papert (1969) proved its limitation: inability to learn XOR.

This limitation sparked the first "AI winter" until the 1980s when multi-layer perceptrons with backpropagation overcame these constraints, leading to modern deep learning.